Enforced Method Acting: Done with the baboons in the first movie. Richard Donner explained that they were having trouble getting the baboons to attack the car. Coincidentally, a veterinarian was there to treat the baboon group's leader, who had been injured in a fight. He suggested to Donner to put the leader in the back of the car in front of the others and make it look like he was being taken away. This sent the baboons into the frenzy shown on-screen. Lee Remick was told that this would happen, but no one expected the baboon leader to actually wake up while in the back of the car and grab her hair. Her screaming during that scene ended up having a very real component to it, as well.
Less traumatically, Donner did this several time with child-actor Harvey Stephens; for example, he provoked Damien's final smile by very emphatically warning Stephens to not smile at the camera.
Shout-Out: The scene in the remake where Kate is hanging onto the railing for dear life and looking up at Damien is similar to Mufasa's death scene in The Lion King. Their dialog is also a bit similar.